SRC/dlaed1.f(3)

NAME
SRC/dlaed1.f

SYNOPSIS

  Functions/Subroutines
subroutine dlaed1 (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info)
DLAED1 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.

Function/Subroutine Documentation

  subroutine dlaed1 (integer n, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, double precision rho, integer cutpnt, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DLAED1 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.

Purpose:

    !>
    !> DLAED1 computes the updated eigensystem of a diagonal
    !> matrix after modification by a rank-one symmetric matrix.  This
    !> routine is used only for the eigenproblem which requires all
    !> eigenvalues and eigenvectors of a tridiagonal matrix.  DLAED7 handles
    !> the case in which eigenvalues only or eigenvalues and eigenvectors
    !> of a full symmetric matrix (which was reduced to tridiagonal form)
    !> are desired.
    !>
    !>   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
    !>
    !>    where Z = Q**T*u, u is a vector of length N with ones in the
    !>    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
    !>
    !>    The eigenvectors of the original matrix are stored in Q, and the
    !>    eigenvalues are in D.  The algorithm consists of three stages:
    !>
    !>       The first stage consists of deflating the size of the problem
    !>       when there are multiple eigenvalues or if there is a zero in
    !>       the Z vector.  For each such occurrence the dimension of the
    !>       secular equation problem is reduced by one.  This stage is
    !>       performed by the routine DLAED2.
    !>
    !>       The second stage consists of calculating the updated
    !>       eigenvalues. This is done by finding the roots of the secular
    !>       equation via the routine DLAED4 (as called by DLAED3).
    !>       This routine also calculates the eigenvectors of the current
    !>       problem.
    !>
    !>       The final stage consists of computing the updated eigenvectors
    !>       directly using the updated eigenvalues.  The eigenvectors for
    !>       the current problem are multiplied with the eigenvectors from
    !>       the overall problem.
    !>

Parameters
    N

    !>          N is INTEGER
    !>         The dimension of the symmetric tridiagonal matrix.  N >= 0.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>         On entry, the eigenvalues of the rank-1-perturbed matrix.
    !>         On exit, the eigenvalues of the repaired matrix.
    !>

    Q

    !>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
    !>         On entry, the eigenvectors of the rank-1-perturbed matrix.
    !>         On exit, the eigenvectors of the repaired tridiagonal matrix.
    !>

    LDQ

    !>          LDQ is INTEGER
    !>         The leading dimension of the array Q.  LDQ >= max(1,N).
    !>

    INDXQ

    !>          INDXQ is INTEGER array, dimension (N)
    !>         On entry, the permutation which separately sorts the two
    !>         subproblems in D into ascending order.
    !>         On exit, the permutation which will reintegrate the
    !>         subproblems back into sorted order,
    !>         i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
    !>

    RHO

    !>          RHO is DOUBLE PRECISION
    !>         The subdiagonal entry used to create the rank-1 modification.
    !>

    CUTPNT

    !>          CUTPNT is INTEGER
    !>         The location of the last eigenvalue in the leading sub-matrix.
    !>         min(1,N) <= CUTPNT <= N/2.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (4*N + N**2)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (4*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = 1, an eigenvalue did not converge
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
     Modified by Francoise Tisseur, University of Tennessee

Definition at line 161 of file dlaed1.f.

Author

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